Lab 1: Classical vs Quantum Information

Tool

• O’Reilly Quantum Simulator

Objectives

• Distinguish classical bits from quantum bits at the level of state
• Explain amplitudes vs probabilities
• Describe measurement and collapse
• Construct and observe an entangled two-qubit state
• Explain what a statevector simulator is simulating

Core Ideas

• Amplitudes define the quantum state
• Probabilities are derived from amplitudes
• Measurement is probabilistic and destructive
• Entanglement means the system cannot be described independently

Part 1: Single Qubit Behavior

1. Start with one qubit in

   0⟩.

2. Apply X and observe.
3. Reset.
4. Apply H and inspect amplitudes.

Questions

• What are the amplitudes after H?
• Are probabilities alone sufficient to describe the state?
• Is the qubit randomly choosing a value before measurement?

Part 2: Measurement and Collapse

1. Prepare H

   0⟩.

2. Measure.
3. Observe post-measurement state.
4. Reset and repeat several times.

Questions

• Does measurement reveal the pre-measurement state?
• Can the superposition be recovered after measurement?
• Why is measurement irreversible?

Part 3: Two Qubits and Entanglement

1. Initialize

   00⟩.

2. Apply H to qubit 0.
3. Apply CNOT (0 control, 1 target).
4. Inspect the state vector.

Questions

• Can this be written as two independent single-qubit states?
• What happens if you measure only one qubit?
• How are outcomes correlated?

What the Simulator Is Doing

• Tracks a complex state vector of size 2^n
• Gates are unitary operations

• Measurement samples using

  amplitude

  ^2

• Does not scale to large n

Submission

• Answers to all questions
• 1 to 2 circuit screenshots
• A brief reflection on quantum vs classical information

Key Takeaway

• Quantum computation is about manipulating and measuring states, not faster classical logic.